One Billion Digits of Pi
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Description: Ramanujan, modular equations, and approximations.
Ramanujan, Modular Equations, and Approximations to Pi How to compute One Billion Digits of Pi*** This article will follow up one small thread of Ramanujan's work which has found a modern computational context, namely, one of his approaches to approximating . Our experience has been that as we have come to understand these pieces of Ramanujan's work, as they have become mathematically demystified, and as we have come to realize the intrinsic complexity of these results, we have come to realize how truly singular his abilities were. This article attempts to present a considerable amount of material and, of necessity, little is presented in detail. We have, however, given much more detail than Ramanujan provided. Our intention is that the circle of ideas will become apparent and that the finer points may be pursued through the indicated references.
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